What is a rhombus? It is known that this is an equilateral quadrangle, which is also a parallelogram. And if the rhombus has all angles equal, then this figure can already be called a square. And all the opposite sides of the rhombus are parallel.
What is a rhombus
A rhombus is an equilateral parallelogram. The word itself is of Greek origin, and means "tambourine." These are round tambourines today, before they were made in the shape of a square. That is why the rhombus has such a name. Also named as a heraldic figure. We turn to the dictionary of Ushakov. What is a rhombus? Compared to a square, it is a rhombus with equal angles. And also a square is a special case of a rhombus. Sometimes they even say that these figures can be compared.
Also associated with the rhombus is the image of the “tambourine” suit on cards that are used in gambling. Also, this figure was used for images on banners, flags and various emblems, but it is much less common than other geometric designs. Today, a rhombus is also used to depict a basketball field. What is a rhombus, we know, but let's look at the properties and signs of this figure.
Rhombus properties
- The rhombus is represented by a parallelogram, all sides of which lie opposite, are equal and parallel.
- The diagonals of this mathematical construction intersect only at right angles and are divided in half at the intersection point. That is, these diagonals divide the rhombus into four absolutely equal triangles.
- The bisectors of the angles are precisely the diagonals.
- The set of squares of the diagonals equals the square of the side, which is multiplied by four.
- The vertices of the rectangle are the midpoints of the four sides of this design called a rhombus.
- The diagonals of the figure are perpendicular to the axes of their symmetry.
- A circle with a center lying at the intersection can be inscribed in any figure called a rhombus.
- What is the diagonal of a rhombus? This is the line that connects its corners.
Signs of a rhombus
We learned what a rhombus is, but in addition to the properties of this figure, there are also signs. Any parallelogram will be a rhombus if it satisfies at least one of the following conditions:
- Two adjacent sides of the rhombus are equal in relation to each other.
- Diagonals of this mathematical construction can intersect only at right angles and nothing else.
- One of the diagonals necessarily bisects all its angles that are contained in it.
- And if we assume that we do not know that the quadrangle is a parallelogram, but it is known that the sides of the figure are equal, then we can confidently say: a quadrangle is a rhombus.
- This is the part of the line that forms an angle equal to 90 degrees when crossing the opposite side.
- What is the height of a rhombus? This is the part of the line that forms an angle of 90 degrees, crossing the opposite side.
Diamond Square
We know what a rhombus is, what are its properties and signs, but how to find its area? In order to find the area of the rhombus, it is necessary to halve the product of the diagonals of this figure. Since a rhombus is the same parallelogram, the area of such a mathematical construction is equal to the product of the height by the length of its sides. In addition, the area of the figure can be found when calculating by formulas with adjacent sides or with a radius of an inscribed circle. The radius of the inscribed circle is expressed through the diagonals. In order to calculate the perimeter of a rhombus, multiply the length of one of the four sides by four.
And in order to depict this figure in the form of a drawing, you must follow the instructions below. Indeed, when building this figure, many have difficulties. So, in order to accurately depict the rhombus, you should first draw the first diagonal, then perpendicular to the second, at the end connect the edges of the segments. You need to carefully and carefully draw this figure, so that instead of a rhombus you do not draw a square.